. In order to project future HIV prevalence and future AIDS cases, to assess effects of risk factors of the HIV epidemic and to evaluate effects of intervention procedures on the HIV epidemic, this application would use stochastic models of the HIV epidemic that take into account the dynamics of the HIV epidemic and the stochastic nature of many variables. This proposal plans to achieve the following three objectives: (i) To develop stochastic models for the spread of HIV that would take into account important characteristics of the behavioral, social and biological aspects of the HIV epidemic. (ii) To characterize the infection distributions of HIV transmission by using stochastic models of the HIV epidemic under various real conditions. (iii) To evaluate the efficiencies and robustness of statistical methods such as the back- calculation method over different infection distributions for estimating HIV prevalence and for projecting future HIV prevalence and future AIDS cases. The investigators will use stochastic models and computer modeling to characterize the HIV infection distribution that would best describe the HIV epidemic.To take into account prior information on the HIV epidemic, both Bayesian method and sampling theory method will be used to characterize HIV infection under various conditions. They will use the San Francisco cohort data available from CDC to assess the effects of risk factors on the HIV infection and to select best subset of covariates which will best describe the HIV infection.In this proposal, they plan also to use the stochastic models and the response surface method to approximate optimal conditions for the prevention of HIV spread via AIDS education.